Maybe you are confusing isolation with damping? Two different concepts, but related. The isolation is due to the spring being "springy", and is basically related to just one other factor: gravity. (Unless you also apply pressure mechanically). The weight of the speaker is due solely to it's mass times gravity, and the static deflection of the spring is due solely to the stiffness of the spring and the weight of the load (once again, baring mechanically applied pressure).

It is ONLY the static deflection of the spring that sets the resonant frequency of the system.

Look at the math, and it becomes very clear:

The equation for the natural resonant frequency of single degree of freedom system with static deflection is simple:

F = 1/2 PI x SQRT (k/m)

where:

k is the stiffness of the spring, and

m is the mass that is resting on the spring, causing static deflection

In turn, the static deflection equation is also simple:

kD = mG

Where:

k is the stiffness

D is the static deflection

G is gravity

m is mass

If you don't know what the stiffness of your spring is, you can flip the equation around to find out:

k = mG/d

(in words; the stiffness of the spring is equal to the mass multiplied by gravity, divided by the deflection)

Substitute all of the above into the first equation, and you get:

F= 1/2 PI SQRT (G/D)

The same as I said above: The resonant frequency depends ONLY on gravity (G) and the stiffness of the spring, and in turn the stiffness has a direct relationship to the static deflection (D), which in turn depends on the weight of the object.

So, in simple terms: since gravity is constant, and PI is a constant, the ONLY thing you need to do to find the resonant frequency, is look at the static deflection.

And that's also dead easy to do! Get a sample of the "spring" you plan to use, put your speaker on top, and see how much it "squashes down"! That will tell you what the resonant frequency will be. So if your sample is 25mm thick, and when you put your speaker on top it "squishes down" to just 20mm thick, then your static deflection is 5mm. Thus you can predict the resonant frequency. You want that to be not more than half the lowest frequency that the speaker produces, and ideally not more than third.

OK, that's the basis, but it gets more complex: obviously if you over-compress the material, it wont be as springy any more: and by the same token, if you don't compress it very much at all, then it won't be very springy. so you need to check the linearity of the material, and find out what range of compression (deflection) it will work for (remain springy). For most materials, you should be OK in the range 15% to 25% compression, but that's just a general guidelines, not written in stone: check with the manufacturer.

So, you need to find a material that will allow you to get the right amount of static deflection for the frequency you want, but where that amount of deflection is within the linear and useful range for the material.

For most materials, you'll find that you need a very thick "spring". Thin ones don't compress enough, or need to be loaded with a LOT of additional mass, to get the necessary static deflection (when gravity alone isn't enough).

OK, so all of the above is about the spring and the frequency and the deflection and the isolation: but

*damping* is an entirely different matter. A spring by itself is "springy"! (duh....) It bounces! But you don't want your speaker to be bouncing around on the pads, so you have to stop the "bounce" without affecting the springiness. Enter damping. Damping absorbs some of the energy in the "bounce".

Think of it this way: if you have a brick hanging from a tough elastic band, and you pull the brick down then let go, it will bounce up and down on the spring for a long time, at the frequency given by the static deflection. Now take that same system and put it at the bottom of a swimming pool: if you pull the brick down now and let it go, it will rise to where it was before, but it won't bounce up and down much, if any: it just returns to the static deflection position and stops. Because the water "damps" the motion (in addition to making the brick rather "damp" too! It's unfortunate that "damp" has two unrelated meanings... I need a better analogy... ).

That's where you seem to be right now: worried about the damping.

So most people think: "Cool! I'll just use a very springy material that also damps the hell out of things!". Bad idea. Because there's no free lunch. It turns out as you increase the damping on a system, you also increase the transmissibility of the system above resonance... that's just a fancy way of saying that it doesn't isolate so well for frequencies above the resonant frequency. The more you damp it, the less it isolates.

To understand this, it's first necessary to go back to what I said before about needing to get your resonant frequency down below half (and preferably below one third) of the lowest significant frequency put out by the speaker. The reason for that "factor of two, or three" advise is simple. At the resonant frequency, a system does not isolate at all, and in fact, it amplifies (if it didn't, musical instruments wouldn't work very well!). That resonant system continues to resonate at frequencies above and below it's own resonance. And for convoluted mathematical reasons, it refuses to isolate until exactly 1.414 times the resonant frequency. Above that, it isolates. Below that, it amplifies. It does not matter how springy, or what spring, or what damping, or what the material is, or how much you load things, or what the temperature is, or anything else: the factor is ALWAYS going to be 1.414.

Why 1.414? Because that's the square root of 2, and if you go back to the equations above, you'll see that all of this springy stuff is calculated with a big "square root" sign in there. I'm not going to bore you with the derivation of that "Square root of 2" thing, but it's easy to remember that your resonant system will

*amplify* below 1.4 times the resonant frequency, and will

*isolate* above that frequency.

Of course, it's not that there's a sudden cut-off at 1.4, with everything below amplifying terribly, and everything above isolating excellently! Rather, there's a gradual curve that crosses over from "amplify" to "isolate" at exactly 1.414 times the resonant frequency.

So far so good. Now for the interesting part: the SLOPE of that curve is defined by the damping. If there is no damping, it is very steep on both sides of the 1.414 point: So you get high resonance, high amplification below that, and high isolation above it. With lots of damping, the amplification is much lower.... but so is the isolation!

And that's the problem. If you use a material that has very high damping, then sure, it won't resonate very well below the 1.414 point, but it also won't isolate very well above the 1.414 point.

The graphs below illustrate that clearly. Below the horizontal line marked as "transmissibilty = 1", you get isolation. Above that line, you get amplification. Exactly on that line, you get neither: sounds just travels through exactly as it was, without being either amplified or isolated. Obviously, what you want is to make sure that the peak of the resonance above the line is as low as possible (so that it amplifies very little, even at resonance), and also you want to make sure that all of the frequencies your speaker produces are as far below the "less than 1" region as you can get them.... which means you want a system that moves the "1.414" point as far over to the left as possible. If you have a highly damped system, that curve below the line rises up towards 1, and flattens out... so you don't get good isolation until maybe 3 or even 4 times the resonant frequency. In an undamped system, that curve drops steeply and becomes more vertical, so you get good isolation even at just twice the resonant frequency... but in that case, the resonance is very strong, which you DON'T want.

In other words: Murphy will get you either way!

With low damping, you don't need to tune resonance so low, but then you have very high amplitude at resonance (high "bounce" in your spring)... and with high damping, you get very low amplitude (not much "bounce"), but poor isolation.

The only solution here, is to tune your resonant frequency very low if you want to use a highly damped material. The higher the damping, the lower you need to tune it.

Summary: tune your system using static deflection. That's what determines the resonant frequency. You need a thick spring to get low resonant frequency. You need damping in your system, to reduce the amplitude of the resonance, and stop the "bounce".... but having high damping means poorer isolation.... so you need to tune lower than you thought.

I'm not sure if that helped you more, or if I just managed to confuse you more!

Hopefully, the former.

- Stuart -